Sunday, August 12, 2007

Kolata disputes sex studies

Noted NY Times science reporter Gina Kolata writes:
Everyone knows men are promiscuous by nature. ...

Surveys bear this out. In study after study and in country after country, men report more, often many more, sexual partners than women.

One survey, recently reported by the federal government, concluded that men had a median of seven female sex partners. Women had a median of four male sex partners. ...

But there is just one problem, mathematicians say. It is logically impossible for heterosexual men to have more partners on average than heterosexual women. Those survey results cannot be correct.

It is about time for mathematicians to set the record straight, said David Gale, an emeritus professor of mathematics at the University of California, Berkeley.
No, there is no logical contradiction. It is quite plausible that men have a higher median number of sex partners, as I've discussed here. It can be explained by a small number of women having a lot of sex partner. That is, most men have more sex partners than most women, but a few slut outdo everyone by a wide margin. That's the way it is with the people I know, anyway.

Kolata gives the explanation that men exaggerate while women minimize their misbehavior. But she ignores other possible explanations, such as men having a different definition from women. These surveys don't usually define a sex act or sex partner, and people really do have different definitions.

Update: A reader cites this:
Women are more likely than men to lie about their sex lives, reveals a new study. ...

Women change their answers depending on whether or not they believe they will be caught out not telling the truth, the researchers found. The number of sexual partners a woman reported nearly doubled when women thought they were hooked up to a lie detector machine.
The reader also gives an example where the median can be different from the mean. A small number of sluts can increase the averages, and increase the median for men, but not affect the measured median for women. But Kolata says:
Dr. Gale added that he is not just being querulous when he raises the question of logical impossibility. The problem, he said, is that when such data are published, with no asterisk next to them saying they can’t be true, they just "reinforce the stereotypes of promiscuous males and chaste females."
The suggestion here is that the study authors are publishing inconsistent data, and failing to even notice that the problem. But that is just not true about the govt study cited above. Here is the USA CDC study. This AP story on it even has a correction:
(This version CORRECTS that figures for lifetime sexual partners were median figures, not averages.)
Now Kolata and Gale should issue a correction because the CDC study measured the median, and it probably is true that men have a higher median number of sex partners than women.

I mentioned this CDC study before here. Justoneminute makes a similar point, and gives a nice explanation as why median and mean are different in this case.


Dr X said...

Hey Roger,

You've got it wrong. Try working out your scenario.

100 men
100 women

2 women each have sex with all 100 men. All of the other women are virgins. That means the men have had an average of 2 partners each

The two women have had sex with one hundred men each. That's two hundred partners between the two of them, averaged over all 100 hundred women yields a mean of 2 partners each for the women. Exactly the mean (average) for men.

The median for men and women would be different and the mode would be different, but the mean (the average) would be 2 partners for the women and 2 partners for the men.

Kolata's experts for the article got one thing wrong, though. There has been research done that may explain the discrepancy -- here The research suggests that men report accurately but that women significantly under-report the number of partners they have had.

Anonymous said...

Dr X is missing the point, and Roger is right.

The Times quotes a Federal study citing differences in reported partners on a MEDIAN basis.

The Times then quotes a misdirected math prof proving conclusively what we all agree on - the MEANS ought to be equal. Fine, but so what? The medians might be different if the tails of the distribution behave wildly, as in the "two sluts" example provided here.

So really - providing an example showing that the median and mean can differ does not exactly rebut Roger's point that, hmm, how to say it, the median and mean can differ.

So we are all on the same side, in opposition to a confused Ms. Kolata of the Times and a presumably embarrassed or irate Prof. Gale of Berkeley.

Tom Maguire

mdchaney said...

As I mentioned over at justoneminute, though, the median would have to be a whole number (i.e. integer) in this case. "12.7" cannot possibly be the median to the question of "how many women have you had sex with" unless one of the men answered "12.7". Remember that the median will always be one of the answers.

It is correct that the answer should be the same for each. But it's incorrect that the numbers cited are medians.

Roger said...

Mdchaney, the CDC study does report integers for the medians. Here is a quote from p.3 of the study: "The median number of lifetime female sexual partners for men was seven and the median number of lifetime male sexual partners for women was four."

Anonymous said...

um... Roger:
mean and median- totally different.

so, don't even try pursuing a "slut" argument to explain data that any elementary school student understands.